Quasi-particle bases of principal subspaces for the affine Lie algebras of types B_l⁽¹⁾ and C_l⁽¹⁾

2015/05/03 by Marijana Butorac, Butorac, Marijana
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.1505.00450

arXiv admin note: text overlap with arXiv:1212.5920

arxiv created 2015/05/03 · openalex publication_date 2015/05/03 · arxiv updated 2015/05/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Generalizing our earlier work, we construct quasi-particle bases of principal subspaces of standard module L_Xl⁽¹⁾(kΛ₀) and generalized Verma module N_Xl⁽¹⁾(kΛ₀) at level k≥ 1 in the case of affine Lie algebras of types B_l⁽¹⁾ and C_l⁽¹⁾. As a consequence, from quasi-particle bases, we obtain the graded dimensions of these subspaces.

Citations

• Local systems of vertex operators, vertex superalgebras and modules
• Combinatorial bases of principal subspaces for affine Lie algebra of type B₂^(1)

Related

• Quasi-particle bases of principal subspaces of the affine Lie algebra of type G₂⁽¹⁾
• A note on principal subspaces of the affine Lie algebras in types B_l⁽¹⁾, C_l⁽¹⁾, F₄⁽¹⁾ and G₂⁽¹⁾
• Combinatorial bases of principal subspaces for affine Lie algebra of type B₂^(1)
• Combinatorial constructions of modules for infinite-dimensional Lie algebras, I. Principal subspace
• Bases of standard modules for affine Lie algebras of type C_ℓ⁽¹⁾